九州大学大学院総合理工学府報告第 38 巻 第 1 号 1-6 頁 平成 28 年 9 月

Engineering Sciences Reports, Kyushu University
Vol. 38, No. 1, pp. 1-6, SEP., 2016

Optical field profile evaluation on silica highhigh-mesa
waveguide for infrared absorption sensing
Hirohito HOKAZONO *1 Haisong JIANG *2, † and Kiichi HAMAMOTO *2†

E-mail of corresponding author: jiang@asem.kyushu-u.ac.jp(Received June 14, 2016, accepted July 1, 2016)

Breathe sensing system that incorporates waveguide gas cells has been proved to be handy for
performing daily breath checks. One critical issue for high-sensitivity breath sensing has been highpropagation loss. We previously proposed the utilization of a silica high-mesa waveguide due to its
low propagation loss. However, till date, few studies have demonstrated that a certain portion of the
propagation light profiles out from the waveguide that contributes to infrared absorption sensing so
far. In this study, we provide experimental evidence that a certain portion of the propagation light
profiles out on an actually fabricated silica high-mesa waveguide for the first time.
Key words: Breath sensing, silica high-mesa waveguide, FFP reverse-Fourier transformation method

1. Introduction
A breath-sensing system incorporating
waveguide gas cells has proved to be handy for
performing daily breath checks.1)-3) One criticalissue for high-sensitivity breath sensing has
been high propagation loss. For instance, in thecase of Si/SiO2 high-mesa waveguide for which
the propagation loss is 0.9 dB/cm (at λ = 1550
nm, w = 0.8 µm), performing high-sensitivity
breath sensing is difficult because thepropagation loss is higher than the gas
absorption4)-5). We previously proposed the useof a silica high-mesa waveguide due to its low
propagation loss, illustated in Fig. 16). The
silica high-mesa waveguide comprises GeO2doped SiO2 core and SiO2 cladding. Relativerefractive index difference (∆n) of the
waveguide in the perpendicular direction is set
as 2.5 %. Low refractive index contrast between
air and the core of the waveguide contributes toless suffering from the side-wall roughness, inaddition to the low absorption loss inherent to
the material. The lateral confinement of the
waveguide is realized by the so-called highmesa structure. Figure 2 shows the optical fieldof a silica high-mesa waveguide simulated*1 Department of Applied Science for Electronics andMaterials, Graduate student*2 Department of Applied Science for Electronics andMaterials

using finite element method (FEM) when the
waveguide width is 2.2 µm. As the side-wall of
the core directly faces to the outside, a certain
portion of optical field propagetes out of the
waveguide (here, we define this value as Γout7)),which is utilized for gas absorption8-9). However,
not enough experimental evidence exits toconfierm the existence of the portion of opticalfield that propagete out of the waveguide. Such

Fig.1
ig.1 Cross sectional view of silica high-mesa
waveguide.

Fig. 2 Optical field of the silica high-mesa waveguide.

Optical Field Profile Evaluation on Silica High-mesa Waveguide for Infrared Absorption Sensing

a portion of optical field only exists at
approximatly 0.2 µm from the waveguide sidewall, as is shown in Fig. 2. Thus, we need tomeasure the optical field of the waveguide crosssection (near field pattern; NFP) with a
precision of around 0.01 µm to detect the
portion of optical field that propagates out ofthewaveguide.
Performing
the
NFP
measureing method with a precition of 0.01 µm
is, however, difficult because it is normallymonitored through a lens system that degrades
the precision in position. Here, we focus on therelation between NFP and far field pattern(FFP) using Fourier transformation. FFP is theangle component of the optical field propagatedfrom the waveguide facet.
In this study, we demonstrate a method formeasuring NFP of optical waveguide byreverse-Fourier transformation of FFP. In
addition, the experimental evidence that acertain portion of optical field propagates out ofwaveguide is obtained by fabricating a silica
high-mesa waveguide for infrared absorption
spectroscopy. Moreover, it is succesfully
confirmed for the first time that 5.8% of the
potical field propagetes out of the waveguide.

2. Optical field profile evaluation
evaluation of
NFP
byreversereverse-Fouriertransformation of the FFP
2.1 Relation between NFP and FFP
Figure 3 shows that the coordinate system of
the Fresnel–Kirchhoff diffraction formula10).
The waveguide facet is located at z = 0. The
output of optical field from the waveguide facet
propagates to the z-axis direction in free space.
When the optical field profile of the NFP is f(x,y, R) and the optcial field profile of the FFP
located in z = R is f(x, y, R), the relation between
NFP and FFP is obtaind using Fresnel–
Kirchhoff diffraction formula as follows:
=

, ,

and

,

,0

exp

(1)
#

=
−
+ −
+ ! "$ ,(2)
where k is the wave number and n is therefractive index in free space. The refractive
index is 1 due to propagation of air in free space.

y

y0

FFP

NFP

f(x, y, R)

f(x0, y0, 0)

x

x0

z

Fig. 3 Coordinate system of Fresnel-Kirchhoff
diffraction formula.

Using the approximation of z >>|x − x0|, |y −y0|, equation (2) is rewritten as follows:= ! %1 +=!+#' '( $ ) * *( $ $' $ )* $+−+$''( )**(
+

, ≅!+

+

'($ )*($+' '( $ ) * *( $
+

+ ⋯.

+⋯

(3)

In Eq. (3), the approximation until the third
term is called FFP or the Fraunhoffer region,and the approximation until the fourth term iscalled the Fresnel region. By approximating Eq.
(1) in Fraunhoffer region, the following
equation is obtained:
, ,

=

/01

×

2+

+

exp 3
,

' $ )* $+, 0 exp 3−

4''( )**(
+

4

. (4)

Thue underlined term in Eq. (4) is ignored
because it is constant at the obsrevation point.
The double-underlined term that represents
the phase delay from the origin to observation
point is omitted because this term tends tounity when calculating the optical intensity.
Thus, the relation between NFP and FFP is
assessed using Fourier transformation.
2.2

ReverseReverse-Fourier transformation of the
FFP to NFPHere, we define the optical field profile of
NFP as fN and the optical field profile of FFP as
fF. In addition, we define x = Rcosθx and y =Rsinθy because FFP is a polar coordinate
component. Equation (4) is rewritten as follows:
6 78' , 8* 9 =× exp;− 7,
sin 8' +:sin 8* 9?

.

(5)On applying reverse-Fourier transformation,
Eq. (5) becomes:,=× exp; 7

6 78' , 8* 9

sin 8' +sin 8* 9? 8' 8*(6)Eq. (6) is not, however, a reverse-Fouriertransformation. Asuuming that sinθx = θx and平成 28 年度

九州大学大学院総合理工学報告

sinθy = θy in case of θx, θy = 0, Eq. (6) becomes asfollows::,=
6 8' , 8'
× exp; 7 8' + 8* 9?

.

(7)Equation (7) shows that FFP converts to NFP
by using reverse-Fourier transformation. To
confirm the reverse-Fourier transformation of
the FFP to NFP, we simulate the NFP using
FEM and the FFP using beam propagation
method (BPM) on the silicon waveguide when
wavelength is 1550 nm (Fig. 4). Figure 5 shows
the optical field and phase of FFP of the silicon
waveguide simulated using BPM. Uisng opticalfield of Fig. 5, we convert FFP to NFP using Eq.
(7). The optical field resulting from theconversion of FFP and the optical field

Fig. 4 Schematic of the silicon waveguide.

第 38 巻

第1号

simulated using FEM are shown in Fig. 6. The
optical field of NFP of FEM and NFP converted
from FFP are appared the difference in vicinityof boundary of core and clad of silicon
waveguide (x = ±1.0µm). The optical field of
NFP, resulting from the conversion of FFP
correspond closely with the optical field of NFP
simulated using FEM. The difference arises
due to the approximation used in Eq. (7).
2.3 Phase of FFP
To convert FFP to NFP, the FFP phase isnecessary. However, the result of measuring
FFP is not phase profile, as in Fig. 5. Since thephase profile in Fig. 5 is constant (320°), it ispossible to assume that the phase profile of FFP
is optional phase constant. Figure 7 shows thatthe result of NFP after using reverse-Fouriertransformation that is used the optical field ofFig. 5 and phase profile of 0° constant. In thisfigure, we confirmed that the optical field of
NFP converted from FFP (phase is 0° constant)closely corresponds to the optical field of NFP
simulated using FEM.
2.4
The conversion
conversion accuracy of reversereverseFourier transformation
In the preceding section, we demonstrated
that the optical field of the waveguide facet is
obtained using reverse-Fourier transformationof FFP to NFP. Next, we comfirmed thepossibility that the conversion accuracy ofreverse-Fourier transformation is a function of
the silicon waveguide width when the width ischanged from 0.4 µm to 5.0 µm. To check theconversion accuracy, we adopted the sample

Fig. 5 Optical field and phase of FFP (Fig. 4) simulatedusing BPM.

Optical field [a.u.]

1.0
0.8
0.6
0.4
0.2
0
-4

Fig. 6 Optical field of NFP of FEM and converted FFP(Fig. 5).

FEM
Converted the
FFP(phase is 0°)-20x-axis [µm]24Fig. 7 Optical field of NFP of FEM and converted the
FFP (Fig. 4 and phase is 0°).

Optical Field Profile Evaluation on Silica High-mesa Waveguide for Infrared Absorption Sensing

B − CB,(8)

Sample variance s2

where n is the plot number of optical field, xi isthe optical field of NFP after conversion from
FFP, and Xi is the optical field of NFP simulatedusing FEM. Figure 8 shows the sample
variance as a function of the waveguide width
obtained using Eq. (8). The sample variance of
optical field becomes 0.0015 constant for a
waveguide width of 2 µm. Thus, we confirmedthat it is possible to convert FFP to NFP for a
waveguide width of 2µm with the sameaccuracy.
0.025
0.002
0.015
0.01
0.005
0

Fig. 80

1
3
4
2
Waveguide width w [µm]5Sample variance of optical field converting the
FFP as a function of waveguide width.

3. The measurement of FFP andconversion to NFP
3.1 Silica highhigh-mesa waveguideIn this section, we explain the fabrication ofasilicahigh-mesa
waveguideusing
measurements of FFP, as is shown in Fig. 1.
Figure 2 shows the optical field of the silica
high-mesa waveguide simulated by FEM when
the waveguide width is 2.2µm and wavelengthis 1572nm. We used the wavelenght of 1572 nm
as we it is the absorption wavelength of CO2. As
is shown in Fig. 2, a certain portion of opticalfield exists out of the waveguide. Thus,
measuring the gas absorption is possible for
applying a certain portion of optical field
propagating out of the waveguide. Hence, we
confirmed that a certain portion of optical field
propagating out of the silica high-mesa
waveguide can be measured by reverse-Fouriertransformation of FFP.

Figure 9 shows the optical field of Fig. 2 andthe conversion of FFP of silica high-mesa
waveguide to NFP by reverse-Fouriertransformation in the x-axis and the direciotn
component in the y-axis (x = 0 µm and y = 6.75µm). The optical field of NFP simulated using
FEM is appeared the discontinuity of opticalfield in vicinity of boundary of core and air ofsilica high-mesa waeguide (x = ±1.1µm), as isshown in Fig. 9(a). The optical field of NFP
converted from FFP is a continuous optical field.
This difference might be due to theapproximation used in Eq. (7). However, we
confirmed that the converted FFP of silica highmesa waveguide corresponds closely to theoptical field of NFP simulated using FEM.
Moreover, using the optical field converted form
FFP, we evaluated the portion of optical fieldthat propagates out of the waveguide.
3.3

Optical field of NFP converted from themeasured FFP

Figure 10 shows the experiment design used
to measure the FFP of the silica high-mesa
waveguide.
Three
dimensional
FFP
1.0
Optical field[a.u.]

∑BD

@ =

3.2 Optical field of NFP converted from the
FFP of BPM

0.8
0.6

FEM
Converted the
FFP(phase is 0° )

0.4
0.2
0
-4

-3

-2

-1
0 1
x-axis [µm]

2

3

4

(a) x-axis of NFP

1.0
Optical field [a.u.]variance. The sample variance (s2) is obtained
as follows: 11)

FEM
Converted the
FFP(phase is 0°)

0.8
0.6
0.4
0.2
0

-5

0

5
y-axis [µm]1015(b) y-axis of NFP
Fig. 9 Optical field of NFP of FEM and converting the
FFP of Fig. 8 (phase is 0°).

平成 28 年度

九州大学大学院総合理工学報告(wavelength is 1572nm) measurements wereobtained via spherical scanning by a photodetector located at the output of the optical fieldfrom the silica high-mesa waveguide. Then, weused the LD 8900, which allows real-timemeasurements of the three-dimensional FFP.
Figure 11 shows that the horizontal andvertical direcition components of the opticalfield of the measured FFP when the waveguide
width is 2.2 µm. Figure 12 shows the NFP
converted from the measured FFP (Fig. 11), thephase is 0°constant. The optical field of NFP
converted from the measured FFP becomeswider than the optical field of NFP obtainedusing FEM. Because FEM simulates the opticalfield for the fundamental mode only. The
optical field propagating the waveguideincludes small high order mode, and high order
Emitted lightPD
Silica high-mesa waveguide

第 38 巻第1号

mode affects both measured FFP and converted
NFP. Another possible reason for this could bethat the photo detector detects the light that
propagates by diffracting from the upper andlower optical waveguide but not the light thatsimulataneously propagates through the core.
However, we experimentally confirmed that acertain portion of optical field propagates out of
the silica high-mesa waveguide, as is shown in
Fig. 12(a). Thus, silica high-mesa waveguidehas the potential to be used for gas sensing byinfrared absorption.

4. Evaluation of a certain portion of
optical field that propagates
propagates out of the
waveguideIn the previous section, we confirmed that
optical field of NFP converted from measured
FFP and FFP obtained using BPM can bemeasured in case of silica high-mesa waveguide.
Using this optical field, we evaluated the
portion of optical field that propagates out of
the waveguide of silica high-mesa waveguide.
The optical field of NFP converted from FFP isFig. 10 Experiment design used to measure the FFP ofsilica high-mesa waveguide.

1.0
Optical field [a.u.]

Optical field [a.u.]

1.0
0.8
0.6
0.4
0.2
0
-90

-60

60

0.4
0.2

air

0
-4

90

Optical field [a.u.]

0.6
0.4
0.2

1.0

0
-30
30
Vertical axis [°]

-2

-1 0
1
x-axis [µm]

air
2

3

4

60

90

(b) y-axis of FFP
Fig. 11 Optical field of FFP of the silica high-mesa
waveguide (waveguide width is 2.2 µm).

FEM
Converted themeasured FFP

0.8
0.6
0.4
0.2
0

-60

-3

Waveguide(a) x-axis of NFP

0.8

0
-90

0.6

(a) x-axis of FFP

1.0
Op tical field [a.u .]

0
-30
30
Horizontal axis [°]FEM
Converted themeasured FFP

0.8

-5

0

5
y-axis [µm]1015(b) y-axis of NFP
Fig. 12 Optical field of NFP by FEM and converted themeasured FFP of silica high-mesa waveguide(waveguide width is 2.2µm).

Optical Field Profile Evaluation on Silica High-mesa Waveguide for Infrared Absorption Sensing

The portion of optical fieldthat propagates out of the
waveguide (Γ out) [%]10

NFP. Furthermore, the photo detector detects
the light propagated by diffraction from theupper and lower optical waveguide but not thelight that is simultaneously propagatedthrough the core.

Converted the measured FFP
Trendline of measured Γout
Converted the FFP (BPM)
FEM

8
6
4

5. Conclusions
Conclusions2
λ = 1572nm

0
2.0

4.5
3.5 4.0
2.5 3.0
Waveguide width w [µm]5.0Fig. 13 The portion of optical field that propagates outof the waveguide (Γout) as a function of
waveguide width.

two-dimensional (x- and y-axis direcition
components). Thus, we converted the twodimensional NFP into a three-dimensional NFP.
Here, the three-dimensional NFP is f(x0,y0); xand y-axis direcition components are fx(x0) andfy(y0). We assumed the three-dimensional NFP
to follow the equation (9):
,

= '

*

.

(9)

Using this eauation (Eq. (9)), we evaluated the
portion of optical field that propagates out of
the waveguide (Γout). Figure 13 shows Γout as afunction of waveguide width for the converted
FFP and the trendline of the measured Γout.
Converting the FFP obtained using BPM andsimulated by FEM. The Γout of the FFP
converted using BPM is only 0.3 % higher thanthe Γout simulated using FEM due to theapproximation used in Eq. (7). Thus, theassumptions made in Eq. (9) used to convert
NFP from two dimensions to three dimensions
are valid because the Γout of both FFPs
substantially correspond. Next, we comparedthe Γout of converting the measured FFP andthe Γout simulated using FEM. The Γout of
converting the FFP using BPM is 3 % higherthat the Γout simulated by FEM. However, we
confirmed that the Γout of the converted
measured FFP decreases with ingcreasing
waveguide width. This trend is the same for Γout
simulated using FEM. FEM simulates the
optical field for the fundamental mode only.
The optical field propagating the waveguideincludes small high order mode, and high ordermode affects both measured FFP and converted

We have proposed a method to measure NFPof optical waveguide using reverse-Fouriertransformation of the FFP. This method
provides experimetal evidence that a certain
portion of optical field propagates out of thesilica high-mesa waveguide for infraredabsorption spectroscopy. The results confirm
that the method to measure NFP of opticalwaveguide by reverse-Fourier transformationof the FFP allows for a certain level ofaccurancy.
Moreover,we
providetheexperimental evidence that 5.8% of optical field
propagetes out of the waveguide (for a
waveguide width of 2.2µm) on fabricated silica
high-mesa waveguide. We concule that thesilica high-mesa waveguide has the potential to
be used for breath sensing.
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